Problem: Simplify; express your answer in exponential form. Assume $t\neq 0, y\neq 0$. $\dfrac{{(t^{-3})^{-2}}}{{(t^{5}y)^{-5}}}$
Answer: To start, try working on the numerator and the denominator independently. In the numerator, we have ${t^{-3}}$ to the exponent ${-2}$ . Now ${-3 \times -2 = 6}$ , so ${(t^{-3})^{-2} = t^{6}}$ In the denominator, we can use the distributive property of exponents. ${(t^{5}y)^{-5} = (t^{5})^{-5}(y)^{-5}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(t^{-3})^{-2}}}{{(t^{5}y)^{-5}}} = \dfrac{{t^{6}}}{{t^{-25}y^{-5}}}$ Break up the equation by variable and simplify. $\dfrac{{t^{6}}}{{t^{-25}y^{-5}}} = \dfrac{{t^{6}}}{{t^{-25}}} \cdot \dfrac{{1}}{{y^{-5}}} = t^{{6} - {(-25)}} \cdot y^{- {(-5)}} = t^{31}y^{5}$.